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I think what you have established here is just that $\rho$ tends to increase with mass. The density of planets isn't constant. Let $\rho = \rho_0 (M/M_{earth})^{\alpha}$, so that $M = (4/3)\pi R^{3} \rho_0 (M/M_{earth})^{\alpha}$ Then $$g = \frac{GM}{R^2} = \frac{4\pi G}{3} R \rho$$ Replace $R$ with $(3M/4\pi \rho)^{1/3}$ so that $$g = \frac{4\pi G}{3} ... 1 For planets of constant mean density you have:$$ M=\rho \times 4\pi r^3 $$and the surface value of g is:$$ g(r)=\frac{GM}{r^2}=G \times \rho\times 4 \pi \times r  So for bodies of constant density the surface gravity is proportional to the radius, and the slope as $r \to 0$ tells you the density. So for bodies of equal density $\log(g(r)) \to -\infty$ ...